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why is $L=\{\{x\mid x<q(i)\}\mid i\in\mathbb{N}\}$ not the set of all Dedekind cuts?
Let the set $L$ be definded as
$$L=\{\{x\mid x<q(i)\}\mid i\in\mathbb{N}\},$$
where $q(i)$ is some bijection from $\mathbb{N}$ to $\mathbb{Q}$.
Clearly, every member of $L$ is neither an empty set ...
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Set representation of (real) numbers [duplicate]
Using the Von Neumann representation we can represent the non-negative whole numbers using the empty set, e.g. $1$ as {$\emptyset$}.
How do we represent with this notation numbers like $\sqrt2, -1, \...
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